Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.7 - Factoring by Special Products - Exercise Set - Page 310: 80

Answer

$\text{area} = (x-y)(x+y)$

Work Step by Step

The area of the shaded region is equal to the difference between the areas of the bigger square and the smaller square. Thus, the area of the shaded region is: $A=\text{area of the bigger square}-\text{area of the smaller square} \\A=x(x) - y(y) \\A=x^2-y^2$ RECALL: $a^2-b^2=(a-b)(a+b)$ Use the formula above where $a=x$ and $b=y$ to have: $\\A=x^2-y^2=(x-y)(x+y)$
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